Physical-guided neural network based on three-fluid model for disturbance wave velocity prediction

doi:10.16085/j.issn.1000-6613.2024-1757

Abstract

Abstract:

Disturbance waves widely exist in evaporators, natural gas and other industrial environments in annular mist flow pattern, among which the disturbance wave velocity is an important parameter for gas-liquid momentum transfer, heat-transfer and friction pressure drop prediction. To improve the predicted accuracy, the physical-guided neural network (PGNN) was proposed based on the three-fluid model, where the gas core mixture parameters and liquid film parameter were revised by considering the effect of droplet entrained in the gas core. For the experiments, flow tests on various carrier gas parameter and liquid flow rate were conducted, the wave velocities were obtained by using dual conductivity ring liquid film sensor, and the droplet entrainment was measured by using the developed liquid film extraction and metering device. The entrainment correlation was developed with the parameters of gas Weber number and liquid Reynolds number. The hyperparameters of the proposed physical-guided neural network was optimized, and the database of 288 set covering various two-phase flow conditions (pipe diameter, operational pressure, physical properties of the medium, flow direction) was used for the prediction. The results indicated that 76.74% data were within ±5.0% error bands and 94.10% data were within ±15.0% error bands. The predicted accuracy and scalability could be largely enhanced for the proposed PGNN method.

Key words: prediction, gas-liquid two-phase flow, neural networks, disturbance wave velocity, entrainment

摘要：

扰动波广泛存在于蒸发器、天然气等环雾状两相流工业环境中，其中扰动波速是气液界面动量传递、传热和摩擦压降的重要参数。为提高扰动波大范围预测精度，本文以气相-液滴-液膜三流体模型为基础，考虑夹带液滴影响对气芯参数和液膜参数进行修正，提出了基于物理引导神经网络（PGNN）的扰动波速预测方法。利用环雾状流实验装置进行不同载气工况和液相流量实验，利用双电导环液膜传感器获得扰动波速，利用液膜提取装置测量液滴夹带率，并以气相韦伯数和液相雷诺数为参数建立了夹带率关联式。对提出的物理引导神经网络进行了超参数优化，利用不同工况（口径、压力、介质物性、流动方向）下的288组公开扰动波数据进行预测，76.74%的数据点在±5.0%误差带以内，94.10%的数据点在±15.0%误差带以内，相较于其他扰动波关联式和机器学习模型，本文提出的PGNN模型预测精度和可拓展性均大大提升。

关键词: 预测, 气液两相流, 神经网络, 扰动波速, 夹带率

CLC Number:

TP212.9

LI Jinxia, RU Haoran, LIU Wenkai, SUN Hongjun, DING Hongbing. Physical-guided neural network based on three-fluid model for disturbance wave velocity prediction[J]. Chemical Industry and Engineering Progress, 2025, 44(4): 1815-1824.

李金霞, 茹浩然, 刘文凯, 孙宏军, 丁红兵. 基于三流体模型物理引导神经网络的扰动波速预测[J]. 化工进展, 2025, 44(4): 1815-1824.

Figures/Tables 15

参数	Kumar等^[4]	Sun等^[7]
扰动波速	$V w = Ψ V s g + V s l 1 + Ψ$	$V w = Ψ' V g c + u ¯ i 1 + Ψ'$
界面滑移速度比参数	$Ψ = 5.5 ρ g ρ l 0.5 R e l R e g 0.25$	$Ψ' = 10.6 ρ g c ρ l 0.5 R e l f R e g' 0.25$
气相特征速度	$V s g = W g A ρ g$	$V g c = W g A c o r e ρ g + W l E A c o r e ρ l$
特征密度	$ρ g$	$ρ g c = ρ g + W l E A c o r e V g c$
液相特征速度	$V s l = W l A ρ l$	$u ¯ i = 1 - E V s l$
气相特征雷诺数	$R e g = V s g ρ g D μ g$	$R e g' = ρ g V g c D μ g$
液相特征雷诺数	$R e l = ρ l V s l D μ l$	$R e l f = ρ l u ¯ i D μ l$

参数	Kumar等^[4]	Sun等^[7]
扰动波速	$V w = Ψ V s g + V s l 1 + Ψ$	$V w = Ψ' V g c + u ¯ i 1 + Ψ'$
界面滑移速度比参数	$Ψ = 5.5 ρ g ρ l 0.5 R e l R e g 0.25$	$Ψ' = 10.6 ρ g c ρ l 0.5 R e l f R e g' 0.25$
气相特征速度	$V s g = W g A ρ g$	$V g c = W g A c o r e ρ g + W l E A c o r e ρ l$
特征密度	$ρ g$	$ρ g c = ρ g + W l E A c o r e V g c$
液相特征速度	$V s l = W l A ρ l$	$u ¯ i = 1 - E V s l$
气相特征雷诺数	$R e g = V s g ρ g D μ g$	$R e g' = ρ g V g c D μ g$
液相特征雷诺数	$R e l = ρ l V s l D μ l$	$R e l f = ρ l u ¯ i D μ l$

D/10^-3m	P/10⁶Pa	V_sg/m·s^-1	V_sl/m·s^-1	数量	介质	流动方向	扰动波速测量不确定度	参考文献
50	0.1~0.7	10~35	0.006~0.6	42	空气、水	水平	±10.6%	[6]
15	0.15~0.35	18.9~37.7	0.0028~0.028	81	空气、水	竖直	±12.5%	[7]
31.8	0.25	23.4~50.7	0.01~0.12	25	空气、水	竖直	—	[10]
9.525	0.1	5.22~22.05	0.056~0.318	36	空气、水	竖直	—	[11]
9.4	0.12~0.4	6~88	0.052~0.577	40	空气、水	竖直	—	[12]
5	0.1	13.6~43.2	0.0013~0.004	24	空气、水	竖直	—	[13]
11	0.1	12~28	0.023~0.089	28	空气、水	竖直	±11%	[14]
11.6×36	0.1	7.5~13.6	0.008~0.027	12	空气、饱和五氟丙烷（R245fa）	竖直	±22.9%	[15]

参数	范围	不确定度	绝对/相对
管径D/10^-3m	15	$± 0.1$	绝对
两个传感器的距离L/10^-3m	30	$± 0.14$	绝对
工作压力P/10³Pa	150~350	$± 0.7$ %	相对
气体密度ρ_g/kg·m^-3	1.79~4.24	$± 2.4 %$	相对
气体表观流速V_sg/m·s^-1	18.86~37.73	$± 2.6 %$	相对
液体表观流速V_sl/10^-3m·s^-1	2.8~28	$± 2.0 %$	相对
液膜的质量流量W_lf/10^-3kg·s^-1	0.44~4.08	$± 3.2 %$	相对
夹带率E/%	4.89~19.06	$± 3.8 %$	相对
气体流量Q_g/10^-3m³·s^-1	1.39~ 6.94	$± 1.0 %$	相对
液相流量Q_l/10^-6m³·s^-1	0~4.72	$± 2.0 %$	相对

参数	范围	不确定度	绝对/相对
管径D/10^-3m	15	$± 0.1$	绝对
两个传感器的距离L/10^-3m	30	$± 0.14$	绝对
工作压力P/10³Pa	150~350	$± 0.7$ %	相对
气体密度ρ_g/kg·m^-3	1.79~4.24	$± 2.4 %$	相对
气体表观流速V_sg/m·s^-1	18.86~37.73	$± 2.6 %$	相对
液体表观流速V_sl/10^-3m·s^-1	2.8~28	$± 2.0 %$	相对
液膜的质量流量W_lf/10^-3kg·s^-1	0.44~4.08	$± 3.2 %$	相对
夹带率E/%	4.89~19.06	$± 3.8 %$	相对
气体流量Q_g/10^-3m³·s^-1	1.39~ 6.94	$± 1.0 %$	相对
液相流量Q_l/10^-6m³·s^-1	0~4.72	$± 2.0 %$	相对

参数	不确定度/%	合成不确定度
液相表观流速V_sl	±2.0	$u c R e l R e l = ± 2.5 %$
液相密度ρ_l	±0.22
管道公称直径D	±0.67
液相动力黏度µ_l	±1.33
气体密度ρ_g	±2.4	$u c W e g W e g = ± 5.6 %$
气相表观流速V_sg	±2.6
液相表面张力系数σ	±0.96
液相质量流量W_l	±2.0	$u c E E = ± 3.8 %$
液膜质量流量W_lf	±3.2

参数	不确定度/%	合成不确定度
液相表观流速V_sl	±2.0	$u c R e l R e l = ± 2.5 %$
液相密度ρ_l	±0.22
管道公称直径D	±0.67
液相动力黏度µ_l	±1.33
气体密度ρ_g	±2.4	$u c W e g W e g = ± 5.6 %$
气相表观流速V_sg	±2.6
液相表面张力系数σ	±0.96
液相质量流量W_l	±2.0	$u c E E = ± 3.8 %$
液膜质量流量W_lf	±3.2

参数	搜索范围	优化结果
层数	2~5	4
每层神经元数	10~30	20
训练次数	1000~10000	10000
学习率	0.0001~0.1	0.001
动量因子	0.5~1	0.9
最小性能梯度	e^-10	e^-10

预测模型	预测公式	重要中间参数
Schubring等^[2]	$V w = 2.55 V s g R e g x - 13$	$x = W g W g + W l$
Ju等^[3]	$V w = 10.1 V s l W e l - 0.392 W e g 0.227$
Wang等^[8]	$V w = Ψ V g c + u ¯ i 1 + Ψ, Ψ = 0.0017 ρ g c ρ l - 0.5 R e l f R e g - 0.24 P s y s t e m P a t m 0.48$	$u ¯ i = 1.8 V s l 1 - α, R e l < 2100 V s l 1 - α, R e l > 2100$
Sun等^[7]	$V w = Ψ' V g c + u ¯ i 1 + Ψ', Ψ' = 10.6 ρ g c ρ l 0.5 R e g' R e l f - 0.25$	$u ¯ i = 1 - E V s l$
Sun等^[9]	$V w = Ψ V s g + V s l 1 + Ψ, Ψ = B P N N ρ g ρ l, R e g, R e l$
本文	$V w = Ψ' V g c + u ¯ i 1 + Ψ', Ψ' = B P N N ρ g c ρ l, R e g', R e l f$

预测模型	预测公式	重要中间参数
Schubring等^[2]	$V w = 2.55 V s g R e g x - 13$	$x = W g W g + W l$
Ju等^[3]	$V w = 10.1 V s l W e l - 0.392 W e g 0.227$
Wang等^[8]	$V w = Ψ V g c + u ¯ i 1 + Ψ, Ψ = 0.0017 ρ g c ρ l - 0.5 R e l f R e g - 0.24 P s y s t e m P a t m 0.48$	$u ¯ i = 1.8 V s l 1 - α, R e l < 2100 V s l 1 - α, R e l > 2100$
Sun等^[7]	$V w = Ψ' V g c + u ¯ i 1 + Ψ', Ψ' = 10.6 ρ g c ρ l 0.5 R e g' R e l f - 0.25$	$u ¯ i = 1 - E V s l$
Sun等^[9]	$V w = Ψ V s g + V s l 1 + Ψ, Ψ = B P N N ρ g ρ l, R e g, R e l$
本文	$V w = Ψ' V g c + u ¯ i 1 + Ψ', Ψ' = B P N N ρ g c ρ l, R e g', R e l f$

模型	R²	MPE/%	MAPE/%	U_nc,pre/%	ξ_5%/%	ξ_15%/%	ξ_30%/%
Schubring等^[2]	0.93	13.39	54.68	58.30	1.04	6.25	18.50
Ju等^[3]	0.72	3.51	22.97	32.32	13.89	36.11	85.41
Wang等^[8]	0.56	2.37	29.62	27.03	17.71	50.34	74.65
Sun等^[7]	0.89	4.48	12.61	18.15	39.58	78.47	93.06
Sun等^[9]	0.85	1.03	7.12	11.50	73.96	89.93	96.18
本文	0.99	0.41	4.29	10.02	76.74	94.10	98.26

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